so im trying to include this file for an application
http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js
would including it as this url slow the load time of my site when using an application that requires it?
as opposed to downloading this file and including it locally
Quite the opposite, Google’s global network of CDN edge servers is almost certain to give you faster average response times even on the first request.
However, you should never use the “latest” URL like that. In order to reliably start serving newer versions when the time comes, the “latest” URL must respond with a very short expires header, which makes return visits even slower than hosting it on your own server.
The full version URL (e.g. http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js) is served with a +1 year expires header. Always use a fully specified version. Make sure to also do that for initial major version revs, like 1.5.0 instead of 1.5.